Finite Group DatabasebetaFinite Group DatabasebetaOrder 22784.
322 conjugacy classes of subgroups; only the 59 normal subgroups are shown.
This group has 322 conjugacy classes of subgroups — too many to draw. Only its 59 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 1. #26022469 | C2 | semidirect |
| 2. #26022464 | C2 | semidirect |
| 3. #26021805 | C2 | semidirect |
| 4. #26018240 | C2 | semidirect |
| 5. #26018237 | C2 | semidirect |
| 6. #26018190 | C2 | semidirect |
| 161. C89 | #12303 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| #26022469 | 2 |
| #26022464 | 2 |
| #26021805 | 2 |
| #26018240 | 2 |
| #26018237 | 2 |
| #26018190 | 2 |
| C89×#3204 | 2 |
| #12303 | 89 |